STATISTICAL LITERACY


UNDERSTANDING STATISTICS

Making sense of statistics is vital for informed decision-making. To build your statistical know-how check out Understanding Statistics on the ABS website. There are some excellent resources contained within these pages, some are very basic, whilst others go in to more depth. There are quizzes, video tutorials and online presentations. A great resource for anyone wanting to know more about statistics and the ABS website.

UNDERSTANDING STATISTICAL CONCEPTS

In today's information-rich society, we encounter statistical information on a daily basis, ranging from unemployment rates, retail figures and cancer rates, to football ladders and cricket scores. Statistics tell interesting stories and enable us to make sense of the world. Statistics are essential for research, planning and decision-making purposes.

There are several concepts that recur throughout the literature on statistical literacy. These fall into four key areas and can be considered in a practical manner as 'criteria' on which to base statistical literacy:

1. Data awareness
2. The ability to understand statistical concepts
3. The ability to analyse, interpret and evaluate statistical information
4. The ability to communicate statistical information and understandings.

In this issue, we will focus on understanding statistical concepts, and examine the difference between mean, median and mode. The centre of a data set is important. It is often useful to know what the value is for most of the sample or population. In the ABS there are two main measures of central location: the mean and the median.

Mean
The mean, or average, is calculated by summing all of the observed values and dividing by the number of observations. The mean is the simplest way to summarise a single variable and it is generally the best measure of central location for purposes of statistical inference.

Median
The median is the middle value of a set of observations. There are as many observations above the median as there are below it. To find the median, observations must be arranged in order of value. Median is useful for variables such as age, income, turnover and housing prices.

Mode
The mode is the most commonly observed data item in a data set. A set of data can have more than one mode. The mode is useful when the most common item, characteristic or value of a data set is required.

Comparing the mean and the median: which is the most appropriate measure to use?

Turning data into information is an essential skill. Communicating statistical information accurately is vital for effective decision making. To ensure integrity, statistical literacy demands that we question how the data are reported and the reliability of conclusions that are drawn. Bad conclusions can still be drawn from good data. Be aware that using basic summary numbers, such as averages, can sometimes be misleading.

Example 1:
If students attending a tutorial group were aged 18, 18, 19, 19, 21, 22 and 51,
the mean age of the group would be 18 + 18 + 19 + 19 + 21 + 22 + 51 = 168 / 7 = 24
the median age of the group would be the middle value of 19.

Which age best represents the average age of the group? In this case, the mean age is distorted by the presence of the mature age student. The median age would be a closer indication of the true average age of the tutorial group.

Example 2:
If houses in Hobart were advertised for sale at $275,000, $295,000, $300,000, $325,000 and $850,000 respectively, using the mean to calculate the average house price would produce a figure of $409,000 (ie. 275,000 + 295,000 + 300,000 + 325,000 + 850,000 = 2,045,000 / 5 = 409,000). This gives an over-inflated impression of house values in Hobart. In reality, the median value of $300,000 would give a much more accurate picture of average house prices.


For further explanation of terms see Statistical Language! (ABS cat. no. 1332.0.55.002)

In upcoming issues of Tasmanian Statistical News we will discuss other statistical literacy concepts in more detail. Meanwhile, if you would like to know more about statistical literacy and its relevance to you, check out the article: What is statistical literacy and why is it important to be statistically literate? as featured in Tasmanian State and Regional Indicators (ABS cat. no. 1307.6) or visit the Understanding Statistics portal on the ABS website.